HO Leontief Paradox

7/21/2019 HO Leontief Paradox

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The Heckscher-Ohlin ModelSome Background

Proposed by Swedish economist Eli Heckscher in a 1919article

Developed by his student Bertil Ohlin in his 1924dissertation

Attempt to explain the first golden age of trade from1890 to 1914

With the ability to ship technology around the world,technological differences can no longer explain whycountries trade

In this chapter, we outline the Heckscher-Ohlinmodel , a model that assumes that trade occursbecause countries have different resources.

Introduction

Our first goal is to describe the Heckscher-Ohlin (HO)model of trade.

The specific-factors model that we studied in theprevious chapter was a short-run model becausecapital and land could not move between theindustries.

In contrast, the HO model is a long-run modelbecause all factors of production can movebetween the industries.


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Our second goal is to examine the empirical evidenceon the Heckscher-Ohlin model.

By allowing for more than two factors ofproduction and also allowing countries to differ intheir technologies, as in the Ricardian model, thepredictions from the Heckscher-Ohlin modelmatch more closely the trade patterns in theworld economy today.

The third goal of the chapter is to investigate how the

opening of trade between the two countries affects thepayments to labor and to capital in each of them.

Introduction

Assumptions of theHeckscher-Ohlin Model

Assumption 1: Two factors of production, labor andcapital, can move freely between the industries.

Labor must earn the same wage across industries

Capital must earn the same rent across industries

Assumption 2: Shoe production is labor-intensive; thatis, it requires more labor per unit of capital to produceshoes than computers, so that LS / K S > LC / K C .


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FIGURE 4-1

Labor Intensity of Each Industry The demand for labor relativeto capital is assumed to be higher in shoes than in computers,LS /K S > L C /K C .These two curves slope down just like regular demand curves,but in this case, they are relative demand curves for labor (i.e.,demand for labor divided by demand for capital).

Assumptions of the Heckscher-Ohlin Model

Assumption 3: Foreign is labor-abundant, by which wemean that the laborcapital ratio in Foreign exceeds thatin Home, L*/ K *> L / K . Equivalently, Home is capital-abundant, so that K / L >K */ L*.

Assumption 4: The final outputs, shoes and computers,can be traded freely (i.e., without any restrictions)between nations, but labor and capital do not movebetween countries.Is this a realistic assumption?


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Assumptions of the Heckscher-Ohlin Model

Assumption 5: The technologies used to produce thetwo goods are identical across the countries.Allows us to focus on a single reason for trade: thedifferent amounts of labor and capital found in eachcountryThe data fit the model better without this assumptionAssumption 6: Consumer tastes are the same acrosscountries, and preferences for computers and shoes donot vary with a countrys level of income.Assume that poorer country will buy fewershoes/computers, but will buy them in the same ratio as awealthier country facing the same pricesUnrealistic, but simplifying

No-Trade EquilibriumProduction Possibilities Frontiers, Indifference Curves, andNo-Trade Equilibrium Price

FIGURE 4-2 (1 of 3)

The Home production possibilitiesfrontier (PPF) is shown in panel (a),and the Foreign PPF is shown inpanel (b).

Because Home is capitalabundant and computers arecapital intensive, the HomePPF is skewed towardcomputers.

Heckscher-Ohlin Model

No-Trade Equilibria in Home and Foreign


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FIGURE 4-2 (2 of 3)

Home preferences are summarizedby the indifference curve, U.

The Home no-trade (or autarky)equilibrium is at point A.The flat slope indicates a lowrelative price of computers, (P C

/P S ) A.

1 Heckscher-Ohlin Model

No-Trade Equilibria in Home and Foreign (continued)


FIGURE 4-2 (3 of 3)

1 Heckscher-Ohlin Model

No-Trade Equilibria in Home and Foreign (continued)

Foreign is labor-abundant and shoes arelabor- intensive, so the Foreign PPF isskewed toward shoes.

Foreign preferences are summarized bythe indifference curve, U* The Foreign no-trade equilibrium is atpoint A*, with a higher relative price ofcomputers, as indicated by the steeperslope of (P* C /P* S )A*.


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Free-Trade EquilibriumHome Equilibrium with Free Trade

FIGURE 4-3 (1of 2) International Free-Trade Equilibrium at Home (continued)

At the free-trade world relative price ofcomputers, (P C /P S )W ,Home produces at point B in panel (a) andconsumes at point C,exporting computers and importing shoes.

Point A is the no-trade equilibrium.The trade triangle has a base equal tothe Home exports of computers (thedifference between the amount producedand the amount consumed with trade,(Q C 2 Q C 3).

Free-Trade EquilibriumHome Equilibrium with Free Trade

FIGURE 4-3 (2 of 2)

The height of this triangle is the Homeimports of shoes (the difference betweenthe amount consumed of shoes and theamount produced with trade, Q S 3 Q S 2).

In panel (b), we show Homeexports of computers equal to zeroat the no-trade relative price, (P C

/P S )A,and equal to (Q C 2 Q C 3 ) at thefree-trade relative price, ( P C /P S )W .

International Free-Trade Equilibrium at Home (continued)


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Free-Trade EquilibriumForeign Equilibrium with Free Trade

FIGURE 4-4 (1 of 2) International Free-Trade Equilibrium in Foreign (continued)

At the free-trade world relative price ofcomputers, (P C /P S )W ,Foreign produces at point B* in panel (a) andconsumes at point C*,importing computers and exporting shoes.

Point A* is the no-trade equilibrium.)The trade triangle has a base equal toForeign imports of computers (thedifference between the consumption ofcomputers and the amount produced withtrade, ( Q* C 3 Q* C2 ).

Free-Trade EquilibriumForeign Equilibrium with Free Trade

FIGURE 4-4 (2 of 2)

The height of this triangle is Foreignexports of shoes (the differencebetween the production of shoes andthe amount consumed with trade, Q* S 2 Q* S 3).

In panel (b), we show Foreign importsof computers equal to zero at the no-trade relative price, ( P* C /P* S )A*, andequal to ( Q* C 3 Q* C 2) at the free-trade relative price , (P C /P S )W .

International Free-Trade Equilibrium in Foreign (continued)


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Free-Trade EquilibriumEquilibrium Price with Free Trade Because exports equal imports,there is no reason for the relative price to change and so this is a free-trade equilibrium .

FIGURE 4-5

The world relative price ofcomputers in the free-tradeequilibrium is determined at theintersection of the Home exportsupply and Foreign importdemand, at point D.At this relative price, thequantity of computers thatHome wants to export, ( Q C 2 Q C 3), just equals the quantity ofcomputers that Foreign wants toimport, ( Q* C 3 Q* C 2).

Determination of the Free-Trade World Equilibrium Price

Effect of Trade on the Wage and Rental of HomeEconomy-Wide Relative Demand for Labor

Effects of Trade on Factor Prices

FIGURE 4-10

The economy-wide relativedemand for labor, RD , is anaverage of the LC /K C and LS /K S curves and lies between thesecurves .The relative supply, L/K, isshown by a vertical line becausethe total amount of resources inHome is fixed.The equilibrium point A, at whichrelative demand RD intersectsrelative supply L/K, determinesthe wage relative to the rental,W/R.Relative

supplyRelativedemand

Determination of Home Wage/Rental


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Effect of Trade on the Wage and Rental of HomeIncrease in the Relative Price of Computers

FIGURE 4-11

Initially, Home is at a no-tradeequilibrium at point A p with arelative price of computers of(P C /P S )A.An increase in the relativeprice of computers to theworld price, as illustrated bythe steeper world price line,

(P C /P S )W , shifts productionfrom point A to B.At point B, there is a higheroutput of computers and alower output of shoes, Q C 2 >Q C 1 and Q S 2 < Q S 1.


Increase in the Price of Computers


FIGURE 4-12 (1 of 2)

An increase in therelative price ofcomputers shifts theeconomy-wide relativedemand for labor, RD 1,

toward the relativedemand for labor in thecomputer industry, LC

/K C .The new relative demandcurve, RD 2, intersectsthe relative supply curvefor labor at a lowerrelative wage, ( W/R) 2.

Effect of a Higher Relative Price of Computers on Wage/Rental


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FIGURE 4-12 (2 of 2)

As a result, the wagerelative to the rental fallsfrom (W/R) 1 to (W/R) 2.The lower relative wagecauses both industries toincrease their labor capital ratios, asillustrated by theincrease in both LC /K C

and LS /K S at the newrelative wage.

Relative supplyNo change

Relative demandNo change in total

Effect of a Higher Relative Price of Computers on Wage/Rental(continued)

Determination of the Real Wage and Real RentalChange in the Real RentalR = P C MPK C and R = P S MPK S MPK C = R/P C and MPK S = R/P S Change in the Real WageW = P

C MPL

C and W = P

S MPL

S MPLC = W/P C and MPL S = W/P S



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Determination of the Real Wage and Real RentalStolper-Samuelson Theorem: In the long run, when allfactors are mobile, an increase in the relative price of agood will increase the real earnings of the factor usedintensively in the production of that good and decreasethe real earnings of the other factor.For our example, the Stolper-Samuelson theorempredicts that when Home opens to trade and faces ahigher relative price of computers, the real rental oncapital in Home rises and the real wage in Home falls. InForeign, the changes in real factor prices are just thereverse.


Changes in the Real Wage and Rental: A Numerical Example

3 Effects of Trade on Factor Prices


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Changes in the Real Wage and Rental: A Numerical ExampleGeneral Equation for the Long-Run Change in Factor Prices Thelong-run results of a change in factor prices can be summarized inthe following equation:

Realwagefalls

Real rentalincreases

Realrentalfalls

Realwageincreases

Realrentalfalls

Realwageincreases

The equations relating the changes in product prices to changes infactor prices are sometimes called the magnification effect becausethey show how changes in the prices of goods have magnified effects

on the earnings of factors:

Free-Trade EquilibriumPattern of Trade Home exports computers, the good that uses

intensively the factor of production (capital) foundin abundance at Home.

Foreign exports shoes, the good that usesintensively the factor of production (labor) found inabundance there.

This important result is called the Heckscher-Ohlin theorem.



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Assumption 1: Labor and capital flow freely betweenindustries a long-run assumption.Assumption 2: The production of some goods is relativelylabor-intensive, as compared with other goods which arecapital-intensive.Assumption 3: The relative amounts of labor and capitalfound in the two countries is the only difference,Assumption 4: There is free international trade in goods,with no transportation costs and no savings.

Assumption 5: The technology for producing any good isthe same across countries, and there are no differences inthe productivity of labor and capital.Assumption 6: Tastes are the same across countries.


The first test of the Heckscher-Ohlin theorem wasperformed by economist Wassily Leontief in 1953, whodeveloped a method of accounting for inputs and outputs.Leontief assumed (correctly) that in 1947 the United Stateswas capital-abundant relative to the rest of the world.Thus, from the Heckscher-Ohlin theorem, Leontiefexpected that the United States would export capital-intensive goods and import labor-intensive goods.What Leontief actually found, however, was just theopposite: the capitallabor ratio for U.S. imports washigher than the capitallabor ratio found for U.S. exports!This finding came to be called Leontiefs Paradox.

Testing the Heckscher-Ohlin Model


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TABLE 4-1

Leontief used the numbers in this table to test the Heckscher-Ohlintheorem. Each column shows the amount of capital or labor needed toproduce $1 million worth of exports from, or imports into, the United Statesin 1947. As shown in the last row, the capitallabor ratio for exports wasless than the capitallabor ratio for imports, which is a paradoxical finding.

Leontiefs Paradox

Leontiefs Test

Leontiefs ParadoxExplanations Technologies are not the same across countries, in

contrast to what the HO theorem and Leontief assumed.Similarly, labor and capital are not the same acrosscountries.

There are many more factors. Leontief ignored landabundance in the United States, and did not distinguishbetween skilled and unskilled labor.

Goods that are capital-intensive in the US may be labor-intensive elsewhere, making measurement hard.

The year 1947 was unusual. The world is not engaged in completely free trade, and

transportation costs can be significant.



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Examining Factor Endowments

To determine whether a country is abundant in a certainfactor, we compare the countrys share of that factor withits share of world GDP.If its share of a factor exceeds its share of world GDP, thenwe conclude that the country is abundant in that factor ,and if its share in a certain factor is less than its share ofworld GDP, then we conclude that the country is scarce inthat factor .


Capital, Labor and Land Abundance

FIGURE 4-6

Country FactorEndowments, 2000Shown here arecountry shares of sixfactors of productionin the year 2000, foreight selectedcountries and the restof the world.

In the first bar graph, we see that 24% of the worlds physical capital in 2000was located in the United States, with 9% located in China, 13% located inJapan, and so on. In the final bar graph, we see that in 2000 the United Stateshad 22% of world GDP, China had 11%, Japan had 8%, and so on.



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Tests of the HO Model North-South Trade : HO predicts capital-abundant countries

would gain the ost b! trading with labor-abundantcountries" but ost trade is between de#eloped nations$

Bowen, Leamer & Sveikauskas (1987) tested %& countries and1% different factors$

' The relati#e proportion of a factor was correlated with thetendenc! to e(port goods intensi#e in that factor$

' The HO Factor-Proportions Theor! works ore often than not"but not o#erwhel ingl!$ For four factors" the prediction was

correct ore than &)* of the ti e" and for se#en theprediction was correct between +)* and &)* of the ti e$ Forone factor" anagerial workers" the prediction was wrong

ore often than it was right$

Differing Productivities across CountriesRemember that in the original formulation of the paradox,Leontief had found that the United States was exportinglabor-intensive products even though it was capital-abundant at that time.One explanation for this outcome would be that labor ishighly productive in the United States and less productivein the rest of the world.If that is the case, then the effective labor force in theUnited States, the labor force times its productivity (whichmeasures how much output the labor force can produce),is much larger than it appears to be when we just countpeople.



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Differing Productivities across CountriesMeasuring Factor Abundance Once Again To allowfactors of production to differ in their productivities acrosscountries, we define the effective factor endowment asthe actual amount of a factor found in a country times itsproductivity:

Effective factor endowment = Actual factor endowment Factor productivity


,sing the Effecti#e Factorspproach

.uppose the ,. has 1/) illion workers and 0%) trillion incapital" while hina has 2)) illion workers and 0+ trillion incapital$

.ince %)31/) 4 +32))" ,. is relati#el! capital-abundant$ 5ut suppose ,. labor is + ti es ore producti#e$ The ,. has

an effecti#e labor force of 2)) 6or hina has an effecti#e laborforce of 1/)7$

.ince %)32)) 8 +32))" the ,. is still relati#el! capital-abundant" and free trade will lead to rising 93 in hina"falling 93 in ,.$

5ut now Factor Price E;uali


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Differing Productivities across CountriesMeasuring Factor Abundance Once AgainTo determine whether a country is abundant in a certainfactor, we compare the countrys share of that effectivefactor with its share of world GDP.If its share of an effective factor exceeds its share of worldGDP, then we conclude that the country is abundant inthat effective factor ; if its share of an effective factor isless than its share of world GDP, then we conclude that

the country is scarce in that effective factor.


Effective R&D ScientistsEffective R&D scientists = Actual R&D scientists R&D spending per scientist

Differing Productivities across CountriesFIGURE 4-7 (1 of 2)

Shown here are countryshares of R&D scientistsand land in 2000, usingfirst the information fromFigure 4.6, and thenmaking an adjustmentfor the productivity ofeach factor acrosscountries to obtain theeffective shares.

China was abundant in R&D scientists in 2000 (since it had 14% of the worldsR&D scientists as compared with 11% of the worlds GDP) but scarce ineffective R&D scientists (because it had 7% of the worlds effective R&Dscientists as compared with 11% of the worlds GDP).


Effective Factor Endowments, 2000


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Differing Productivities across CountriesFIGURE 4-7 (2 of 2)

Shown here are countryshares of R&D scientistsand land in 2000, usingfirst the information fromFigure 4.6, and thenmaking an adjustmentfor the productivity ofeach factor acrosscountries to obtain theeffective shares.

The United States was scarce in arable land when using the number of acres(since it had 13% of the worlds land as compared with 22% of the worlds GDP)but neither scarce nor abundant in effective land (since it had 21% of theworlds effective land, which nearly equaled its share of the worlds GDP).


Effective Factor Endowments, 2000

,sing the .ign Te(t for Effecti#eFactors

Tref er (199!) e(a ined >> countries and nine factors$ If a countr!?s share of the world?s suppl! of an effecti#e factor

is greater than the countr!?s share of world @AP" then HOpredicts the countr! should e(port that good$ This was testedwith a si ple sign 6B 3 -7 test$

Trefler found that all countries had ore factors 6/%*7passing the sign test than failing it" and it was ore likel! tobe true when the countr! was less de#eloped$

This suggests that the HO odel C adDusted for effecti#efactors C e(plains o#er half of international trade" but thereare other e(planations to consider if we want to e(plain therest$


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Differing Productivities across CountriesEffective Arable Land

TABLE 4-2

This table shows that U.S. food trade has fluctuated between positive andnegative net exports since 2000, which is consistent with our finding that theUnited States is neither abundant nor scarce in land. Total agriculture trade(including nonfood items like cotton) has positive net exports, however.


U.S. Food Trade and Total Agricultural Trade, 20002009

Leontiefs Paradox Once Again

FIGURE 4-8

Shown here are the share oflabor, effective labor, and GDPof the US and the rest of theworld in 1947. The US had only

8% of the worlds population, ascompared to 37% of the worldsGDP, so it was very scarce inlabor. But when we measureeffective labor by the totalwages paid in each country,then the United States had 43%of the worlds effective labor ascompared to 37% of GDP, so itwas abundant in effective labor.

Labor Abundance

% Testing the Heckscher-Ohlin Model

Labor Endowment and GDP for the United States and Rest of World, 1947


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Leontiefs Paradox Once AgainLabor Productivity

FIGURE 4-9

Shown here are estimatedlabor productivities acrosscountries, and theirwages, relative to theUnited States in 1990.Notice that the labor andwages were highlycorrelated acrosscountries: the points

roughly line up along the45-degree line.


Labor Productivity and Wages

Leontiefs Paradox Once AgainLabor Productivity

FIGURE 4-9 (revisited)

As suggested by Figure 4-9, wages across countriesare strongly correlatedwith the productivity of

labor. We use the wagesearned by labor tomeasure the productivityof labor in each country.Then the effective amountof labor found in eachcountry equals the actualamount of labor times thewage.

% Testing the Heckscher-Ohlin Model

Effective Labor Abundance


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Aifferences in Preferences The HO odel assu es that preferences do not differ

between countries" but what if the! do I agine two identical countries" Ho e and Foreign"

producing and G$ Their PPFs look the sa e$ If Ho e has a stronger preference for than Foreign"

then their autark! price ratio P(3P! will be higher$ This

will lead to higher relati#e factor prices for the sector?sintensi#e factor$ ountries can gain fro trade b! OT speciali


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Are Factor Intensities the Same acrossCountries?While much of the footwear in the world isproduced in developing nations, the UnitedStates retains a small number of shoefactories.

In India, the sewing machine used to producefootwear is cheaper than the computer used in a call center. Footwearproduction in India is labor-intensive as compared with the call center,which is the opposite of what holds in the United States.

This example illustrates a reversal of factor intensities between thetwo countries.

In the United States, agriculture and mining are capital-intensive. Inmany developing countries, they are is labor-intensive.

Despite its nineteenth-centuryexterior, this New Balance factoryin Maine houses advanced shoe-manufacturing technology.

Increasing eturns

The HO Model assu es that industries ha#e constantreturns to scale" and this leads to di inishing returnswhen one factor increases in proportion to another$

9hat if a big industr! has increasing returns to scaleThe ore the industr! produces" the lower its M $

This can lead to a strange PPF that bends inward$ ountries can gain fro speciali


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The Product ife !cle

The Product ife !cle

The odel is about fir s" but can be applied tocountries$

The ,. is assu ed to ha#e a co parati#e ad#antage innew product de#elop ent because it has an effecti#e

abundanc! of JA scientists" large product and capitalarkets" and efficient distribution s!ste s$ In earl!

stages" the ,. will tend to e(port the good when it isskilled-labor intensi#e$

s a product atures" production beco es orestandardi


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The @ra#it! Model ewton?s e;uation:

@ra#itational force is e;ual to aconstant ti es the product ofthe two asses" di#ided b! thedistance s;uared$

O#erlapping Inco es

If goods #ar! in ;ualit!" consu ers a! ha#e certaine(pectations consistent with their inco es$

onsider three countries" " 5" and $ is labor-abundant" capital-scarce" and poor$ 5 is inter ediate" with so e poor and so e rich

consu ers$ is capital-abundant" and rich$

The HO Theore would predict ost trade would occurbetween and $

The O#erlapping Inco es H!pothesis predicts trade wouldoccur between and 5" and between 5 and $


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Opinions toward Free TradeAn increase in the relative price of exports will benefit skilledlabor in the long run, regardless of whether these workersare employed in export-oriented industries or import-competing industries .In the long run, then, the skill level of workers shoulddetermine their attitudes toward free trade.

In a survey conducted in the United States by the NationalElections Studies (NES) in 1992, workers with lower wagesor fewer years of education are more likely to favor importrestrictions, whereas those with higher wages and moreyears of education favor free trade.

APPLICATION

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HO Leontief Paradox